We studied here on some simple examples the interaction between valuation family, parameters and ranking result. The ranking method studied is based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. The valuation method considered was introduced initially by the Yager and Filev. This valuation consists in the integration over α-levels, of the average of each α-cut weighted by a weight distribution function. We finish by introducing a new weight distribution function.
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Detyniecki et al. (2000) studied this question.
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